
where \(\pi _b\)  is the behavior policy, \(d_{\pi _b ,\gamma }^{P^{*}}\)  is the offline-data distribution, and \(\omega (s,a) \triangleq \frac{d_{\pi ,\gamma }^{P^{*}}(s,a)}{d_{\pi _b,\gamma }^{P^{*}}(s,a)}\) 
is the marginal importance weight (MIW) between the offline-data distribution and the stationary state-action distribution of the policy \(\pi \)  [1]}, [2]}.

